Chi-square tests worksheet with answers

Free printable Chi-square tests worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A die is rolled 60 times to test whether it is fair. The counts of each face are shown. Compute the chi-square goodness-of-fit statistic χ² for H₀: each face has probability 1/6.

n = 60k = 6

χ² =

2.Easy

A die is rolled 120 times to test whether it is fair. The counts of each face are shown. Compute the chi-square goodness-of-fit statistic χ² for H₀: each face has probability 1/6.

n = 120k = 6

χ² =

3.Medium

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “night shift, major”.

row total = 57column total = 43N = 161

E =

4.Medium

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “rural, high”.

row total = 70column total = 51N = 169

E =

5.Hard

The table shows observed counts. Test at α = 0.01 whether the two variables are independent (no continuity correction). Compute the test statistic χ², then compare it with the critical value from the table.

N = 2803 × 2α = 0.01

χ² =

6.Hard

A chi-square goodness-of-fit test compares observed counts in 4 categories with fully specified expected proportions (no parameters are estimated from the data). How many degrees of freedom df does the test have?

k = 4

df =

Answer key

1. χ² = 4
2. χ² = 3.5
3. E = 15.22
4. E = 21.12
5. χ² = 32.92
6. df = 3

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